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1998 Canada National Olympiad
2
Equation of exponents
Equation of exponents
Source: Canada 1998
March 4, 2006
algebra unsolved
algebra
Problem Statement
Find all real numbers
x
x
x
such that:
x
=
x
−
1
x
+
1
−
1
x
x = \sqrt{ x - \frac{1}{x} } + \sqrt{ 1 - \frac{1}{x} }
x
=
x
−
x
1
+
1
−
x
1
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